Table Of ContentSeries on Quality, Reliability & Engineering Statistics
SYSTEM AND
BAYESIAN
RELIABILITY
Essays in Honor of
Professor Richard E. Barlow
th
on His 70 Birthday
Editors
World Scientific
SYSTEM AND
BAYESIAN
RELIABILITY
SERIES IN QUALITY, RELIABILITY & ENGINEERING STATISTICS
Series Editors: M. Xie (National University of Singapore)
T. Bendell (Nottingham Polytechnic)
A. P. Basu (University of Missouri)
Published
Vol. 1: Software Reliability Modelling
M. Xie
Vol. 2: Recent Advances in Reliability and Quality Engineering
H. Pham
Vol. 3: Contributions to Hardware and Software Reliability
P. K. Kapur, Ft. B. Garg & S. Kumar
Vol. 4: Frontiers in Reliability
A. P. Basu, S. K. Basu & S. Mukhopadhyay
Forthcoming title
Reliability Optimization & Design of Fault Tolerant Systems
H. Pham
Series on Quality, Reliability & Engineering Statistics
SYSTEM AND
BAYESIAN
RELIABILITY
Essays in Honor of
Professor Richard E. Barlow
on His 70th Birthday
Editors
Yu Hayakawa
Victoria University of Wellington, New Zealand
Telba Irony
Food and Drug Administration, USA
Min Xie
National University of Singapore, Singapore
V^ World Scientific
lSa New Jersey London* Singapore' Hong Kong
Published by
World Scientific Publishing Co. Pte. Ltd.
P O Box 128, Farrer Road, Singapore 912805
USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
SYSTEM AND BAYESIAN RELIABILITY
Copyright © 2001 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright
Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to
photocopy is not required from the publisher.
ISBN 981-02-4865-2
Printed in Singapore by World Scientific Printers
Foreword
In the modern world we usually take for granted the reliability of the equip
ment that we use: the freezer will continue to preserve our food whilst we
are away, the airplane engine will keep operating when we are in the air,
even the computer will continue functioning, though the software may occa
sionally play us tricks. Much of this reliability is due to the skill of engineers
in the design of the equipment and in the use of suitable materials in their
construction; the failures, when they do rarely occur, are often due to hu
man error. Engineering skill is often unappreciated and taken for granted,
so that when an engineering failure does occur, as recently happened in
the construction of a foot bridge over the Thames in London, we express
astonishment at the disaster.
There is a body of opinion which holds that if the engineering is done
properly and the equipment sensibly used, then failures need never arise.
This is false; uncertainty is an integral part of all aspects of life and is openly
recognized in, for example, quantum physics and Mendelian genetics, and
engineering is no exception. Failure is an uncertain phenomenon whose
occurrence cannot be predicted nor entirely prevented. Even a bridge can
fail. Once uncertainty enters the picture, it is essential to use the tools of
probability because, as de Finetti and others have shown, probability is
the only satisfactory language in which to speak about uncertainty and,
in particular, the uncertainty that even the skill of the engineer cannot
entirely avoid. There has therefore grown up a discipline which studies, by
probabilistic methods, the manner in which breakdowns occur, how they
can be reduced in number, and how experiments on new products can be
designed so that there is a trustworthy guide to how they will behave in
practice. The subject is usually called Engineering Reliability and Richard
Barlow chose it as the title of his most recent book, although, as he says,
"it is really about statistics". Barlow has been a leader in this field and
VI Foreword
progress in it owes much to the ideas he has developed in the course of his
career.
The first encounter I can recall between us arose when he used a statisti
cal method that, in my view, was unsound and, never being shy of declaring
what appeared to be an error, I said so. Two interesting things then hap
pened; first, my view was sensible, second that view was listened to, neither
event being as frequent as I might wish. As a result, he obtained a grant, an
activity at which he was very successful, his success being indicative of the
high regard in which his work was held by his peers, that took me to visit
him in Berkeley. This was to be the first of many such visits he organized,
making my formal retirement from London both enjoyable and rewarding.
Many hours we have spent together in the Cafe Espresso, just down the
road from Etcheverry Hall and opposite the campus of the University of
California at Berkeley, discussing questions of technical interest to us both.
Neither Dick nor I are great on small talk and we would concentrate on such
vital issues as the correct interpretation of probability, its role in engineer
ing reliability, the proper analysis of data and why, with a few honourable
exceptions, members of the department of statistics over the way were, in
our view, wrong. Reliability theorists and reliability engineers tend to deal
with abstract issues, whereas engineers are better at material matters, and
they tend to work in isolation, so that the gathering together over coffee,
or tea in England, serves not just a social function, but can be integral to
the development of sound research.
Barlow obtained a master's degree in mathematics at Eugene, Oregon in
1955 and a doctorate at Stanford in 1960. There he worked with Sam Karlin
and began the interaction with Frank Proschan that continued for many
years afterwards. After a brief spell outside academia, Barlow obtained a
post at Berkeley in 1963, where he remained until his recent retirement.
As others have discovered, once settled in Berkeley why should one leave?
Here is one of the world's leading universities, in a place with an excellent
climate, in a society which is more sensible, that is, left-wing, than most
in the United States. Only the threat of an earthquake could disturb the
idyll, and after all that is a topic worthy of study by a reliability engineer.
Problems in probability divide into two types; those of direct probability
and those of inverse probability. The division has been recognized ever
since the earliest serious studies of the subject, and first arose after the
introduction of the binomial distribution. If the probability of success in
Foreword vu
each of a number of trials is known as p, then in n trials, judged independent
given p, r the number of successes will be binomial. This is a direct problem,
passing from a known probability p to uncertainty regarding the data, r out
of n. The corresponding inverse problem is, having observed r and n, what
can be said about p, an early solution being due to Bayes. Nowadays it is
common to think of the direct problems as being in the field of probability,
whereas the inverse ones belong to statistics.
Both types arise in engineering reliability. For a single component, the
reliability is commonly described by its failure rate, the equivalent of p in the
binomial example above, and different forms of this function lead directly to
different observed patterns of failure, the analogue of r and n. The problems
become more interesting, and more realistic, when many components are
put together in the form of a coherent structure, when it is required to assess
the behaviour of the structure in terms of those of its components and their
interactions. An interesting early result obtained by Barlow, jointly with
Marshall and Proschan, was that components with failure rate increasing
with time formed, under convolution, a structure with the same increasing
property. In contrast, even in systems with parallel components, increasing
failure rates of components does not imply the property for the system.
The concept of increase on average has been found more useful, as have
realistic bounds on failure rates. Thus invariance does not always obtain
with coherent structures and Barlow has been responsible for many of our
advances in understanding the failure patterns of systems; for example,
in fault-tree analysis. A major contribution has been made with Marshall
on obtaining inequalities and crossing properties of survival functions with
increasing failure rate, enabling useful bounds to be put on the occurrence
of failures.
These are all direct problems but equally he has been responsible for
influential studies of statistical, inverse questions; indeed, his last book is
mainly devoted to this field. An important concept here is the total time
on test and how it changes with time. A more recent enthusiasm has been
the use of influence diagrams which enable the structure of a system to be
more easily appreciated. Some of his work has been in co-operation with
the Lawrence Livermore Laboratory, where he has analysed reliability data
from experiments conducted there, including accelerated life tests where
significant contributions have been made to the relationship between the
reliability in the field and that in the stressed, laboratory environment.
Vlll Foreword
A topic that embraces both the direct and inverse concepts of proba
bility is that of decision analysis, which impinges on reliability in the de
velopment of maintenance systems. When should equipment be withdrawn
from service for maintenance? How extensive should be repair be? When is
it sensible to replace a component? These questions need both a statistical
analysis of experience in the field, and development of a model, in order to
construct sensible strategies.
A common, basic assumption in the literature is that, conditional on
parameters, observations are independent and identically distributed. Re
cent work Barlow has done with Mendel escapes from this assumption and
develops finite tools more relevant to practice. This depends on the earlier
work of de Finetti and makes reliability move even further into the subjec
tive appreciation of probability and what is nowadays called the Bayesian
viewpoint.
The subject of reliability engineering today is very different from the
form it took in the early days of operational research and much of this
change has been due to the work of Richard Barlow. In this volume several
of his colleagues and friends, who appreciate his considerable contributions,
recognize their value by writing papers that build on the work he has done
over the last forty years. Many are former students of his, which reminds
us to recognize the significant effect Barlow has had on reliability studies
through the effort and enthusiasm he has put into teaching many people
who have gone on to do important work in the field. In writing the Foreword
to this important volume, I would like to express my thanks to a person
who has flattered me by not only listening to what Savage, Ramsey, de
Finetti and the other great contributors to our proper understanding of
probability, as elaborated by me in the coffee shop, but who has gone on to
incorporate their ideas into engineering with such important consequences.
May you have a very happy seventieth birthday Dick and see in this volume
the respect with which you and your work is held.
London, August 2001 Dennis V. Lindley
Foreword
Richard Barlow is a professor emeritus in the College of Engineering at
the University of California, Berkeley. He has had a long and distinguished
career. Since 1963 he has been a professor jointly in the Department of
Industrial Engineering and Operations Research and in the Department
of Statistics at UC, Berkeley and in addition a research engineer in UC,
Berkeley's Engineering Systems Research Center. He served as a consultant
to the U. S. Department of Defense and for nearly 30 years he also acted as
a consultant to Lawrence Livermore National Laboratory. In 1991 he was
awarded the von Neumann prize, (together with Frank Proschan).
His book Mathematical Theory of Reliability (published in 1965 and
re-issued in the SIAM classic series in 1996) written jointly with Frank
Proschan and their 1975 book Statistical Theory and Reliability and Life
Testing are major contributions in the field. They are probably the most
widely referred literature in reliability theory worldwide. The latter book
has been translated into German, Russian and Chinese. So many Barlow
and Proschan joint works have been cited that Frank Proschan once in
troduced himself: "I am Proschan. Many people think my first name is
Barlow."
Richard earned a B.A. and an M.A. in mathematics from Knox College
and the University of Oregon respectively. Two years of graduate study
in statistics at the University of Washington was followed by a Ph.D. in
statistics from Stanford University in 1960. It was during his time at Stan
ford that he began his collaboration with Frank Proschan which resulted in
the two books previously mentioned and numerous papers in many areas
of reliability. Richard also has an extensive bibliography of papers on his
own and with other co-authors which have been published in the leading
statistical journals. He and his associates introduced a number of key ideas
in modern reliability theory. Among these are:
IX
